A delayed reaction to a two-finger tap on a trackpad is caused by MacOS waiting to see if you are going to do a single two-finger tap or a double two-finger tap. Essentially, it thinks you might do another two-finger tap and it doesn't want to show the menu when you might be in the middle of a different gesture.
To speed it up, go to System Preferences > Trackpad > Scroll & Zoom and uncheck "Smart zoom." This will disable a feature that lets you zoom in on a specific thing (like a paragraph on a webpage) with a double two-finger tap.
Otherwise, if you want to keep Smart zoom enabled, you can wait the second for the context menu to appear with a two-finger tap, or you can do a two-finger click to make it faster.
As a side note, a similar thing happens on iOS devices. If you have an accessibility shortcut triggered by a triple-press of the home button, then double-pressing the home button is slower to bring up the app switcher. (This may be slightly different on the iPhone X which lacks a home button.)